We have proposed a cross-bridge model of muscle contraction in which during each cycle of ATP hydrolysis, the myosin cross-bridge alternates between a state which binds strongly to actin and a state which binds weakly to actin. Relaxation occurs when the transition between the two states is blocked. In the present study, we have tested several aspects of this model using myosin subfragment-one (S-1) cross-linked to actin; S-1 cross-linked to actin behaves kinetically as if it were at infinite actin concentration. Most important, our results show that, over a wide range of temperature and ionic strength, the rate-limiting step in the acto-S-1 ATPase cycle is equal to the rate at which a muscle fiber redevelops force after a quick stretch. This provides evidence that, as we proposed previously, the rate-limiting step in the acto-S-1 ATPase cycle in vitro controls the curvature of the force-velocity curve determined in vivo. We also studied 0-18 exchange during ATP hydrolysis by the cross linked S-1 and our results suggest that, if our kinetic model is valid, rotation of the phosphate group at the active site of myosin may be inhibited by the presence of actin.